相关论文: From Double Pushout Grammars to Hypergraph Lambek …

Traditional language model alignment methods, such as Direct Preference Optimization (DPO), are limited by their dependence on static, pre-collected paired preference data, which hampers their adaptability and practical applicability. To…

Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary…

In J. Sci. Comput., 81: 2188-2212, 2019, we considered a superconvergent hybridizable discontinuous Galerkin (HDG) method, defined on simplicial meshes, for scalar reaction diffusion equations and showed how to define an interpolatory…

Sesqui-pushout (SqPO) rewriting along non-linear rules and for monic matches is well-known to permit the modeling of fusing and cloning of vertices and edges, yet to date, no construction of a suitable concurrency theorem was available. The…

Hyperedge-Replacement grammars (HR) have been introduced by Courcelle in order to extend the notion of context-free sets from words and trees to graphs of bounded tree-width. While for words and trees the syntactic restrictions that…

We study combinatorial Dyson Schwinger equations, expressed in the Hopf algebra of words with a quasi shuffle product. We map them into an algebra of polynomials in one indeterminate L and show that the leading log expansion one obtains…

Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, De Raedt et al's ProbLog and Vennekens et al's LPAD, combines statistical and logical knowledge representation and inference. Inference in these…

Direct Preference Optimization (DPO) aligns Large Language Models with human preferences without the need for a separate reward model. However, DPO treats all tokens in responses equally, neglecting the differing importance of individual…

We introduce two extensions of the $\lambda$-calculus with a probabilistic choice operator, $\Lambda_\oplus^{cbv}$ and $\Lambda_\oplus^{cbn}$, modeling respectively call-by-value and call-by-name probabilistic computation. We prove that…

Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…

We consider the graph $k$-colouring problem encoded as a set of polynomial equations in the standard way over $0/1$-valued variables. We prove that there are bounded-degree graphs that do not have legal $k$-colourings but for which the…

The article is devoted to the magnitude homology of digraphs, with a primary focus on diagonal digraphs, i.e., digraphs whose magnitude homology is concentrated on the diagonal. For any digraph $G$, we provide a complete description of the…

The Lov\'asz Local Lemma is a powerful probabilistic technique for proving the existence of combinatorial objects. It is especially useful for colouring graphs and hypergraphs with bounded maximum degree. This paper presents a general…

We introduce ConfPO, a method for preference learning in Large Language Models (LLMs) that identifies and optimizes preference-critical tokens based solely on the training policy's confidence, without requiring any auxiliary models or…

Graphs can be used to describe complex systems. Recently, whole graph embedding (graph representation learning) can compress a graph into a compact lower-dimension vector while preserving intrinsic properties, earning much attention.…

Diffusion large language models (dLLMs) are promising alternatives to autoregressive large language models (AR-LLMs), as they potentially allow higher inference throughput. Reinforcement learning (RL) is a crucial component for dLLMs to…

Document-level relation extraction typically relies on text-based encoders and hand-coded pooling heuristics to aggregate information learned by the encoder. In this paper, we leverage the intrinsic graph processing capabilities of the…

Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…

We introduce the two substructural propositional logics KL, KL+, which use disjunction, fusion and a unary, (quasi-)exponential connective. For both we prove strong completeness with respect to the interpretation in Kleene algebras and a…

In this paper, we investigate the expressive power and the algorithmic properties of weighted expressions, which define functions from finite words to integers. First, we consider a slight extension of an expression formalism, introduced by…